Cryptology ePrint Archive: Report 2011/672

Fast and Secure Root Finding for Code-based Cryptosystems

Falko Strenzke

Abstract: In this work we analyze five previously published respectively trivial
approaches and two new hybrid variants for the task of finding the roots of the error locator polynomial
during the decryption operation of code-based encryption schemes. We compare
the performance of these algorithms and show that optimizations concerning
finite field element representations
play a key role for the speed of software implementations.
Furthermore, we point out a number of timing attack vulnerabilities that
can arise in root-finding algorithms, some aimed at recovering the message,
others at the secret support. We give experimental results of software
implementations showing that
manifestations of these vulnerabilities are present in straightforward
implementations of most of the root-finding variants presented in this
work.
As a result, we find that one of the variants provides security with respect to
all vulnerabilities as well as competitive computation time for code parameters that minimize the public key size.